Problem: Rewrite as a simplified fraction. ${0.4\overline{67} = {?}}$
Let $x$ equal the decimal. Set up two equations such that the digits after the decimal point are identical. ${\begin{align*}1000x &= 467.6767...\\ 10x &= 4.6767...\end{align*}}$ Subtracting the two equations, we have: ${990x = 463}$ ${x = \dfrac{463}{990}} $